Incompressible Canonical Quantization

Details Incompressible Canonical Quantization Incompressible Canonical Quantization

2002-10-11

arxiv.org/abs/math-ph/0210025v1

Physics

Mathematical Physics

12 Pages

Scientific paper

The notion of incompressible momentum observables is introduced. It is shown that when the metric in a manifold has a certain form, a set of canonically conjugate variables Xk and Pk in which Pk are incompressible, can be constructed. Based on this set of variables, the quantum mechanical description of the motion of a particle in a manifold, is identical to that associated with the familiar canonically conjugate variables xk and pk in an Euclidean space with Cartesian coordinates. The controversy related to non-uniqueness of momentum operators when the range of a coordinate is a finite interval is reduced to two possible extensions. This suggests relating these two types of extensions to the type of particle as being fermion or boson.

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